Embracing the Wide Sky is Daniel Tammet's perplexing sequel to his extraordinary memoir Born on a Blue Day (2006), in which he recounted his childhood experiences as an autistic savant, his epilepsy, his synaesthesia and his ability to recite pi to its 22,514th decimal place. Born on a Blue Day was a short book that had a big impact: it was remarkable because it gave a unique insight into what it might feel like to be an autistic savant. Now Tammet goes further: in Embracing the Wide Sky he attempts to describe what it thinks like to be a savant.

The book, as perhaps befits its subject, doesn't just range or roam widely, it leaps like a chamois, hops like a grenouille, and skips like a carefree child, a faulty CD or a free-associating professor teaching Everything on a course in All Knowledge in the University of Life.

What really matters in the book are Tammet's detailed descriptions and analyses of his own excellings in memory, language and mathematics, but along the way there are long detours into various highways and byways in neuroscience and psychology, taking in constraint-induced movement therapy, developments in brain-imaging, theories of creativity and language acquisition, genius sperm-banks and chess-playing computers, with Tammet drawing largely and generously on the work of VS Ramachandran, Antonio Damasio and Noam Chomsky. He off-roads even further with a chapter on the pointlessness of IQ tests, and goes out of his way to be scathing about Oliver Sacks - or at least he would if his prose ever rose to scathing. What's remarkable is that Tammet's many wanderings seem always measured and logical. His response to what he feels is Sacks's misleading portrayal of savants in his 1985 book The Man Who Mistook His Wife for a Hat is typically reasonable: "The best one can say of this description ... is that it is distinctly unsympathetic."

The best one can say of the early part of Embracing the Wide Sky is that it is perfectly entertaining. There is little evidence of Tammet having conducted any original research, and his conclusions from his wide reading are oddly banal: "what our brains help give us, more than anything else, is our own uniqueness and the myriad tastes and talents that emerge from it. What we do with them, and how, is part of the adventure of becoming ourselves"; "I believe that everyone is born with certain talents, which dedication and hard work help to realise."

The book becomes truly fascinating, and frustrating, when Tammet begins his own detailed self-commentary. In a widely reported comment at the time of the publication of Born on a Blue Day, Professor Allan Snyder, from the Australian National University in Canberra, explained Tammet's significance thus: "Savants can't usually tell us how they do what they do. It just comes to them. Daniel can. He describes what he sees in his head. That's why he's exciting. He could be the Rosetta Stone." Embracing the Wide Sky promises decryption of the myriad mysteries of the mind: what we get, in fact, is just a glimpse, a pin-hole view of a vast and complex process.

Tammet attempts to explain, for example, exactly how he can learn a foreign language in only a week. He says he uses what he calls "elaborative encoding", which involves analysis, association and deep comprehension, rather than mere rote learning. He explains that this process involves listening to songs and practising saying the words - which is surely pretty much what happens in your average secondary school language lab, where children struggle to pass a GCSE in French after five years. Similarly, he claims that his number abilities "are linked to activity in the region of my brain responsible for syntactical organisation", and describes how the well-known process of "chunking" information might help others to discern the patterns and beauties in maths. But reciting pi, to 22,514 places? The mystery remains. Tammet describes himself at one point in the book as "one of the world's few well-known autistic savants". He remains, in fact, unknowable.

• Ian Sansom's The Delegates' Choice is published by Harper Perennial. To order Embracing the Wide Sky for £15.99 with free UK p&p call Guardian book service on 0330 333 6846.